Place eggplant slices in a colander; sprinkle both sides of each slice with salt. Allow to sit for at least 3 hours. Wipe excess moisture from eggplant slices with paper towels.
Preheat oven to 350 degrees F (175 degrees C). Grease a baking sheet.
Mix bread crumbs and 1/4 cup Parmesan cheese together in a bowl.
Dip eggplant slices in beaten egg; coat with bread crumb mixture. Arrange coated eggplant slices in a single layer on the prepared baking sheet.
Bake in the preheated oven until lightly browned and crisp, about 5 minutes per side.
Cover the bottom of a 9x13-inch casserole dish with a layer of spaghetti sauce; top with a layer of eggplant slices. Sprinkle with about 1 tablespoon of the remaining Parmesan cheese and 1/3 the mozzarella cheese. Repeat layers with remaining ingredients, ending with a cheese layer. Sprinkle with basil.
Bake in the preheated oven until cheese is bubbling and golden brown, about 35 minutes.